We define a new topological invariant of an embedded torus in a homology , analogous to the Levine–Tristram invariant of a knot. We compare it to an invariant of smooth tori, defined recently by Echeverria using gauge theory for singular connections.
"A Levine–Tristram invariant for knotted tori." Algebr. Geom. Topol. 22 (5) 2395 - 2418, 2022. https://doi.org/10.2140/agt.2022.22.2395